Restriction theorems for semistable sheaves

2022/04/04 by Mihai Pavel, Pavel, Mihai
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2204.01762

Abstract

In this paper we prove restriction theorems for torsion-free sheaves that are (semi)stable with respect to the truncated Hilbert polynomial over a smooth projective variety. Our results apply in particular to Gieseker-semistable sheaves and generalize the well-known restriction theorems of Mehta and Ramanathan. As an application we construct a moduli space of sheaves in higher dimensions.

Related

• Boundedness of semistable sheaves
• Moduli spaces of slope-semistable pure sheaves
• Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
• A restriction theorem for torsion-free sheaves on some elliptic manifolds
• Uniform boundedness of semistable pure sheaves on projective manifolds